a) Approximate the area under graph (a) of $f(x)=3 / x^{2}$ over the interval $[1,5]$ by computing the area of each rectangle to four decimal places and then adding.

Step 1 ：First, we need to understand that the area under the curve of a function can be approximated by the sum of the areas of rectangles under the curve. The width of each rectangle is the interval divided by the number of rectangles, and the height is the function value at the left endpoint of each rectangle.

Step 2 ：The interval is $[1,5]$, so the width of each rectangle is $5-1=4$.

Step 3 ：The height of each rectangle is $f(x)=3 / x^{2}$, so we need to calculate the function value at the left endpoint of each rectangle.

Step 4 ：The left endpoint of the first rectangle is $x=1$, so the height of the first rectangle is $f(1)=3 / 1^{2}=3$.

Step 5 ：The left endpoint of the second rectangle is $x=5$, so the height of the second rectangle is $f(5)=3 / 5^{2}=0.12$.

Step 6 ：The area of the first rectangle is $width imes height = 4 imes 3 = 12$.

Step 7 ：The area of the second rectangle is $width imes height = 4 imes 0.12 = 0.48$.

Step 8 ：The total area under the curve is the sum of the areas of the rectangles, which is $12 + 0.48 = 12.48$.

Step 9 ：Therefore, the approximate area under the graph of $f(x)=3 / x^{2}$ over the interval $[1,5]$ is $12.48$.

Step 10 ：Finally, we check that our result meets the requirements of the problem. The problem asks for the area to be approximated to four decimal places, and our result is indeed to four decimal places. Therefore, our result meets the requirements of the problem.

Step 11 ：\boxed{12.48}